Long and Short Time Behavior of Non-local in Time Subdiffusion Equations

IF 1.6 2区数学 Q2 MATHEMATICS, APPLIED

Applied Mathematics and Optimization Pub Date : 2024-03-25 DOI:10.1007/s00245-024-10116-7

Juan C. Pozo, Vicente Vergara

引用次数: 0

Abstract

This paper is devoted to studying the long and short time behavior of the solutions to a class of non-local in time subdiffusion equations. To this end, we find sharp estimates of the fundamental solutions in Lebesgue spaces using tools of the theory of Volterra equations. Our results include, as particular cases, the so-called time-fractional and the ultraslow reaction-diffusion equations, which have seen much interest during the last years, mostly due to their applications in the modeling of anomalous diffusion processes.

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非局部时间亚扩散方程的长短时间行为

本文致力于研究一类非局部时间亚扩散方程解的长短时间行为。为此，我们利用 Volterra 方程理论的工具，找到了 Lebesgue 空间中基本解的尖锐估计值。我们的结果包括所谓的时间分数方程和超慢速反应扩散方程，这些方程在过去几年中备受关注，主要是因为它们在异常扩散过程建模中的应用。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Applied Mathematics and Optimization 数学-应用数学

CiteScore

3.30

自引率

5.60%

发文量

103

审稿时长

>12 weeks

期刊介绍： The Applied Mathematics and Optimization Journal covers a broad range of mathematical methods in particular those that bridge with optimization and have some connection with applications. Core topics include calculus of variations, partial differential equations, stochastic control, optimization of deterministic or stochastic systems in discrete or continuous time, homogenization, control theory, mean field games, dynamic games and optimal transport. Algorithmic, data analytic, machine learning and numerical methods which support the modeling and analysis of optimization problems are encouraged. Of great interest are papers which show some novel idea in either the theory or model which include some connection with potential applications in science and engineering.